Theorems · Definition · category theory

CategoryTheory.Functor.mapTriangleIso

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.HasShift C ℤ] →
          [inst_3 : CategoryTheory.HasShift D ℤ] →
            {F₁ F₂ : CategoryTheory.Functor C D} →
              (e : F₁ ≅ F₂) →
                [inst_4 : F₁.CommShift ℤ] →
                  [inst_5 : F₂.CommShift ℤ] →
                    [CategoryTheory.NatTrans.CommShift e.hom ℤ] → F₁.mapTriangle ≅ F₂.mapTriangle

Two isomorphic functors F₁ and F₂ induce isomorphic functors F₁.mapTriangle and F₂.mapTriangle if the isomorphism F₁ ≅ F₂ is compatible with the shifts.

Defined in

Mathlib.CategoryTheory.Triangulated.Functor

Cited by

8 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Functor.CommShiftCategoryTheory.NatTrans.CommShift